典型储液类结构流-固耦合问题的扩展研究

Extended research on fluid-solid coupling problems of typical liquid storage structure

为了明晰流体与固体耦合力学机理及其相互作用力,本文以典型储液类流固耦合问题为研究对象,综合应用变积方法、Lagrange乘子法和对合变换法,建立了非保守流固耦合问题的一类变量和二类变量的拟变分原理。经推导其驻值条件得到一类变量和二类变量流固耦合问题的控制方程。应用Lagrange乘子表示流固耦合界面处耦合因子,分别给出应用流体力学变量和固体力学变量表达的耦合因子。将拟变分原理应用于有限元素法,建立了流-固耦合动力学的协调元和杂交元计算模型。本文对流固耦合问题的变分方法发展和提高计算效率具有重要作用。

In order to clarify the mechanical mechanism and interaction of fluid solid coupling problems,methods of variational integral method,Langrange multiplier method and involutory transformation were applied synthetically to establish the quasi-variational principles with one or two kinds of variables for typical Non-conservative nonlinear fluid-solid coupling problems of liquid storage structures.Governing equations for the fluid-solid coupling problems with one or two types of variables were obtained by deriving their stationary conditions.Coupling factors were ex-pressed using Lagrange multipliers at the fluid-structure interface and described separately with fluid mechanics and solid mechanics variables.The quasi-variational principles were applied to the finite element method by developing computation models with compatible and hybrid elements separately for fluid-solid coupling dynamics.This study is crucial for advancing variational methods in fluid-solid coupling research and improving computational efficiency.